The Unified Transform and the Water Wave Problem
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Publication:3294749
DOI10.1007/978-3-030-33536-6_3zbMath1444.76033OpenAlexW2990669270MaRDI QIDQ3294749
Konstantinos Kalimeris, Athanassios S. Fokas
Publication date: 29 June 2020
Published in: Nonlinear Water Waves (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-030-33536-6_3
Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Research exposition (monographs, survey articles) pertaining to fluid mechanics (76-02) Basic methods in fluid mechanics (76M99) Free-surface potential flows for incompressible inviscid fluids (76B07)
Cites Work
- Quaternions, evaluation of integrals and boundary value problems
- The solution of the modified Helmholtz equation in a wedge and an application to diffusion-limited coalescence
- A Riemann-Hilbert approach to the Laplace equation
- Computing eigenvalues and eigenfunctions of the Laplacian for convex polygons
- A class of unified transform techniques for solving linear elliptic PDEs in convex polygons
- Boundary value problems for Boussinesq type systems
- Boundary value problems for the elliptic sine-Gordon equation in a semi-strip
- On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains
- On the integrability of linear and nonlinear partial differential equations
- Two–dimensional linear partial differential equations in a convex polygon
- A high–order perturbation of surfaces (HOPS) approach to Fokas integral equations: Three–dimensional layered–media scattering
- Well-posed two-point initial-boundary value problems with arbitrary boundary conditions
- The solution of linear constant-coefficient evolution PDEs with periodic boundary conditions
- The instability of periodic surface gravity waves
- Synthesis, as Opposed to Separation, of Variables
- A Novel Non-Local Formulation of Water Waves
- A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain
- The Fundamental Differential Form and Boundary-Value Problems
- Water waves over a variable bottom: a non-local formulation and conformal mappings
- The Dbar formalism for certain linear non-homogeneous elliptic PDEs in two dimensions
- Methods for Solving Elliptic PDEs in Spherical Coordinates
- Absolute and Convective Instability for Evolution PDEs on the Half‐Line
- The Heat Equation in the Interior of an Equilateral Triangle
- A new transform method II: the global relation and boundary-value problems in polar coordinates
- Lax pairs: a novel type of separability
- A unified transform method for solving linear and certain nonlinear PDEs
- A new transform method for evolution partial differential equations
- On a transform method for the Laplace equation in a polygon
- A Hybrid Analytical-Numerical Technique for Elliptic PDEs
- Explicit integral solutions for the plane elastostatic semi-strip
- The modified Helmholtz equation in a semi-strip
- Extending the unified transform: curvilinear polygons and variable coefficient PDEs
- Water waves with moving boundaries
- The Poisson and the Biharmonic Equations in the Interior of a Convex Polygon
- Stokes flow singularities in a two-dimensional channel: a novel transform approach with application to microswimming
- A numerical technique for linear elliptic partial differential equations in polygonal domains
- The nonlinear Schrödinger equation with t -periodic data: I. Exact results
- The nonlinear Schrödinger equation with t -periodic data: II. Perturbative results
- The Spectral Dirichlet--Neumann Map for Laplace's Equation in a Convex Polygon
- The inverse water wave problem of bathymetry detection
- The Method of Fokas for Solving Linear Partial Differential Equations
- A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs
- The basic elliptic equations in an equilateral triangle
- The spectral representation of two-point boundary-value problems for third-order linear evolution partial differential equations
- On a new non-local formulation of water waves
- A transform method for linear evolution PDEs on a finite interval
